A car dealer who sells only late-model luxury cars recently hired a new salesperson and believes that this salesperson is selling at lower markups. He knows that the long-run average markup in his lot is $5,600. He takes a random sample of 16 of the new salesperson's sales and finds an average markup of $5,000 and a standard deviation of $800. Assume the markups are normally distributed. What is the value of an appropriate test statistic for the car dealer to use to test his claim?

Question

Quizplus · Accepted Answer

The appropriate test statistic is a t-test because the population standard deviation is unknown and the sample size is relatively small. The test statistic is calculated using the formula: $t = \frac{\bar{x} - \mu}{(s/\sqrt{n})}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $s$ is the sample standard deviation, and $n$ is the sample size. Plugging in the given values: $t = \frac{5000 - 5600}{(800/\sqrt{16})} = \frac{-600}{200} = -3$.

A Car Dealer Who Sells Only Late-Model Luxury Cars Recently